A general guide in Bayesian and robust Bayesian estimation using Dirichlet processes

Abstract

In this paper, we investigate Bayesian and robust Bayesian estimation of a wide range of parameters of interest in the context of Bayesian nonparametrics under a broad class of loss functions. Dealing with uncertainty regarding the prior, we consider the Dirichlet and the Dirichlet invariant priors, and provide explicit form of the resulting Bayes and robust Bayes estimators. Tractability of the results is supported by numerous examples of different well-known loss functions. The practical utility of the proposed Bayes and robust Bayes estimators are examined for a real data set.